Question

The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by $y=\left(4 t-2 t^{2}\right) m$ and $x=(3 t)$ metre, where $t$ is in second and point of projection is taken as origin. The angle of projection of projectile with vertical is

• A. $30^{\circ}$
• B. $37^{\circ}$
• C. $45^{\circ}$
• D. $60^{\circ}$

Answer 1

Answer: (B)

$y=4 t-2 t^{2}$
$x=3 t$
$V=V_{x \hat{i}}+V_{y \hat{j}}$
$V_{x}=\frac{d x}{d t}, V_{y}=\frac{d y}{d t}$
$V_{x}=3, V_{y}=4-4 t$
for $t=0, V_{y}=4$
$\tan \theta=\frac{V_{y}}{V_{x}}=\frac{4}{3}$
$\theta=53^{\circ}$ with horizontal With vertical
$\theta=37^{\circ}$